APK Download: towelroot.com
1. Download towel root apk from towelroot.com.
2. Run towel root and let it install the SU binary
3. Download and install Super SU apk version 2.0 from playstore or here.
4. Run super SU and let it update its binary by normal method (no recovery needed if super SU version is 2.0+).
5. Reboot and run Super SU yet again and go to settings to move Super SU into /system as a system apk.
6. Reboot to get full root as system app.
7. Install recovery and busybox (busybox should not be installed in case of using [nut]'s dual recovery).
Steps provided by Cookie Ninja. (Modified a bit by me)
and that's pretty much it. Installed recovery, Updated my Binary through TWRP and I'm all set. (You can update it through the normal method now. It's fixed!)
I've tested this on my Xperia Z (C6603) Locked Bootloader running 4.4.2 Stock Kitkat 10.5.A.0.230
Confirmed Working for LB 4.4.2 and 4.3.
If you're looking to root 4.4.4, please follow this guide by KingVortex